Are large animals more likely to become extinct than small animals?
Are large animals more likely to become extinct than small animals?
Ideal is probably somewhere in between…
These are all comparative questions that we can test by comparing different species.
This is the classical way people studied biodiversity - e.g. Darwin, Wallace etc.
When you fit a linear regression you assume your data points are independent…
But if your points are species they are not…instead you find close relatives often cluster together.
If you treat gorillas and chimps as independent, you count all the evolution which occurred on the red branch twice etc.
Two main methods
Residual errors should have:
Normal distribution (univariate)
Multivariate normal distribution
\(\lambda\) transforms the tree by multiplying the off-diagonal elements (internal/shared branches) of the vcv matrix by \(\lambda\)
Tree remains the same = trait is evolving under Brownian motion (BM)
This is the same as independent contrasts
Tree collapses to a star phylogeny = trait is not related to phylogeny
This is the same as an OLS model
Internal branches get shorter = there is phylogenetic signal in the trait but not as much as under BM.
Pattern where related species resemble each other more than more distant relatives
Note this is a pattern not a process (Kamilar & Cooper 2013; Losos 2011)
Two most used methods are:
\(\frac{MSE_0}{MSE}\) is different for every tree as it depends on tree size and shape
Therefore we divide this by the expected value under Brownian motion so we can compare trees.